The long-term goal of this project continues to be the development and evaluation of appropriate new methodologies for the resolution of genetic and non-genetic determinants of complex diseases and disease-related traits, and an investigation of how genes and environments interact to product phenotypic variation. Arguably, this may be the single most outstanding challenge in genetic epidemiology today. Towards this end, the specific aims cover theoretical/methodological issues in linkage and association analysis, optimum study designs suitable for complex traits, and evaluations of important methodological issues through simulations and occasional applications to read data. The proposed theoretical methodological studies include the development of mathematical and statistical tools for the analysis of phenotypic and genotypic data: extensions of the powerful variance components linkage models in SEGPATH to incorporate categorical phenotypes (logistic model), survival phenotypes with censored data (proportional hazards), semi-quantitative traits, multilocus etiological models, and multivariate phenotypes; development and extensions of suitable meta-analysis methods for pooling results from multiple genome-wide linkage/association scans; optimum study designs and sampling strategies suitable for detection of complex trait genes of modest effect sizes in the face of gene-gene and gene-environment interactions; development of methods for the resolution of genetic heterogeneity by subdividing a sample into relatively more homogeneous subgroups (CART and cluster analysis); development of novel methods for sub-localization of trait genes using a two-stage design and dense maps of single nucleotide polymorphisms (SNPs); development of non-parametric methods for linkage analysis of sibships where some sibs are "affected" while others have a quantitative measurement (semi-quantitative); development of novel sequential methods for analysis and interpretation of a genome wide scans, with particular attention to a balance between false positives and false negatives. A number of simulations (and some real data) studies are proposed to evaluate the potential strengths and weaknesses of various theoretical models developed so as to identify specific areas for further methodological research, and to evaluate some outstanding methodological issues that do not readily lend themselves to theoretical investigations. We believe that consideration of multiple approaches to the same complex problem as proposed here constitutes a strength and improves robustness of the inference, and further, that the proposed research will contribute significantly to the advancement of genetic epidemiology.